In continuous casting of steel, it is very important to determine at which position in a continuously cast product is completed solidification of the continuously cast product (hereinafter referred to as a “crater end”). The reason is that detection of the crater end contributes to greatly improving productivity and quality of the cast product.
For example, when the casting speed is increased to improve productivity, the crater end is moved downstream in the casting direction of the cast product. If the crater end exceeds the range of rolls supporting the cast product, the cast product is bulged by the action of static iron pressure (hereinafter referred to as “bulging”) and internal quality is deteriorated. In the event of giant bulging, shutdown of the casting process may be caused. Accordingly, if the crater end is not definitely confirmed, the casting speed cannot be increased beyond a conservatively set level.
Also, in soft reduction operation aiming to reduce central segregation in a cast product and to achieve higher quality, the casting speed and the intensity of secondary cooling water have to be controlled so that the crater end is positioned within a soft reduction zone. Further, in the case of a slab having a compressed shape, it is known that the crater end is not uniform in the transverse direction of the slab and the shape of the crater end is varied with time. Such a variation in the shape of the crater end is also a major factor deciding the quality and productivity of the slab.
Because of the necessity of determining solidification of a cast product (hereinafter referred to also as a “slab”) in order to meet the above-mentioned requirements, various methods for determining solidification of the slab have been proposed so far.
A currently generally practiced method comprises the steps of performing calculation based on the heat condition equation in solidifying a slab and estimating, as the crater end, a position where the temperature in a central portion of the slab represents the solidus (see, e.g., Patent Document 1).
A method for directly measuring the crater end online is also tried. For example, Patent Document 2 discloses a method comprising the steps of propagating an ultrasonic longitudinal wave through a slab by using a transmitter and a receiver for electromagnetic ultrasonic, and determining respective thicknesses of a solid phase and a liquid phase from the following formula (1) based on the propagation time of an ultrasonic longitudinal wave signal passing through a slab, the thickness of the slab, and the previously-measured ultrasonic velocities of the longitudinal wave in the solid phase and the liquid phase. In the formula (1), d is the thickness of the solid phase, t is the propagation time, D is the thickness of the slab, V1 is the average ultrasonic velocity of the longitudinal wave in the liquid phase, and VS is the average ultrasonic velocity of the longitudinal wave in the solid phase.
                    d        =                                            (                              t                -                                  D                                      V                    1                                                              )                                      2              ×                              (                                                      1                                          V                      S                                                        -                                      1                                          V                      1                                                                      )                                              ⁢          Λ                                    (        1        )            
Patent Document 3 discloses a method for estimating the crater end based on the correlation among the thickness of the solid phase (=thickness of a solidified shell) determined as described above, the distance in the lengthwise direction of the casting process, and the amount of change in the thickness of the solid phase. Further, Patent Document 4 discloses a method comprising the steps of, in consideration of temperature dependency of the ultrasonic velocity of the longitudinal wave in the solid phase, calculating an average value of the ultrasonic velocity from a temperature distribution of the solid phase, and determining the thickness of the solid phase with high accuracy by using that average value.
In addition, there is proposed a method comprising the steps of propagating an ultrasonic shear wave through a slab by using a transmitter and a receiver for electromagnetic ultrasonic, and determining whether the crater end has reached the position where the transmitter and the receiver for electromagnetic ultrasonic are installed, by utilizing such a property that the shear wave does not propagate through the liquid phase (see, e.g., Patent Documents 5 and 6).                Patent Document 1: Japanese Unexamined Patent Application Publication No. 5-123842        Patent Document 2: Japanese Unexamined Patent Application Publication No. 55-158506        Patent Document 3: Japanese Unexamined Patent Application Publication No. 57-32863        Patent Document 4: Japanese Unexamined Patent Application Publication No. 2-55909        Patent Document 5: Japanese Unexamined Patent Application Publication No. 63-313643        Patent Document 6: Japanese Unexamined Patent Application Publication No. 2002-14083        